Related papers: On Mixing Constructions with Algebraic Spacers
We adapt the arguments of Marcus, Spielman and Srivastava in their proof of the Kadison-Singer problem to prove improved paving estimates. Working with Anderson's paving formulation of Kadison-Singer instead of Weaver's vector balancing…
The algebraic expression $3 + 2 + 6$ can be evaluated to $11$, but it can also be partially evaluated to $5 + 6$. In categorical algebra, such partial evaluations can be defined in terms of the $1$-skeleton of the bar construction for…
In this paper we study partitions whose successive ranks belong to a given set. We enumerate such partitions while keeping track of the number of parts, the largest part, the side of the Durfee square, and the height of the Durfee…
In this work, we prove a refinement of the Gallai-Edmonds structure theorem for weighted matching polynomials by Ku and Wong. Our proof uses a connection between matching polynomials and branched continued fractions. We also show how this…
A conjecture regarding the structure of expander graphs is discussed.
We present three methods to construct majorizing measures in various settings. These methods are based on direct constructions of increasing sequences of partitions through a simple exhaustion procedure rather than on the construction of…
For paired comparison experiments involving competing options described by two-level attributes several different methods of constructing designs having block paired observations under the main effects model are presented. These designs are…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer $n\geq 1$ there is a continuum of topological dimension $n$ supporting a transitive completely scrambled…
Results concerning recurrence and ergodicity are proved in an abstract Hilbert space setting based on the proof of Khintchine's recurrence theorem for sets, and on the Hilbert space characterization of ergodicity. These results are carried…
We present an algebraic structure in modules over integer rings with cardinality prime powers, which allows to define bases. With such structure, we prove a similar version for the basis extension theorem of linear algebra over fields.…
We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of M\"oller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
We derive mixing properties for a broad class of Poisson count time series satisfying a certain contraction condition. Using specific coupling techniques, we prove absolute regularity at a geometric rate not only for stationary…
This work studies the relationship between the chains of an algebraic lattice and the order structure of the join-semilattice of its compact elements. The results are presented into four chapters, each corresponding to a paper written in…
We study a representation of the (local) plactic monoid given by Schur operators $u_i$, which act on partitions by adding a box in column $i$ (if possible). In particular, we give a complete list of the relations that hold in the algebra of…
In a previous paper by the author a universal ring of invariants for algebraic structures of a given type was constructed. This ring is a polynomial algebra that is generated by certain trace diagrams. It was shown that this ring admits the…
Polynomial meshes (called sometimes "norming sets") allow us to estimate the supremum norm of polynomials on a fixed compact set by the norm on its discrete subset. We give a general construction of polynomial weakly admissible meshes on…
We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible structures on the strictly upper triangular matrix algebra $UT_n(K)$ for all $n\ge 3$.
This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…